Interval Definition and 677 Threads

dy/dx=(sinx)/y Initial condition is y(pi/2)=1 The solution to the IVP is y=(1-2cosx)^.5 That I know is correct, but they're saying the interval of existence is when pi/3<x<5*pi/3. Is that wrong? I think it should include the π/3 and 5π/3.

Homework Statement In the Home Frame, two events are observed to occur with a spatial separation of 12ns and a time coordination separation of 24ns. A)An inertial clock travels between these events in such a manner as to be present at both events. What timer interval does this clock read...

Homework Statement Find the radius of convergence and interval of convergence of the series: as n=1 to infinity: (n(x-4)^n) / (n^3 + 1) Homework Equations convergence tests The Attempt at a Solution i tried the ratio test but i ended up getting x had to be less than 25/4 ...

Homework Statement Give an example of an indexed family of sets such that the intersection of any finite subfamily is not empty, but the intersection when the index=infinity, is empty. The Attempt at a Solution The family I came up with is the exclusive interval (-1/k , 1/k) where...

Homework Statement Consider the following intervals: A = [-3,5), B = (3,8), C = (0,4] Find: A\capB and A\capC The Attempt at a Solution I thought that: A\capB=(3,5) and that A\capC=[0,4] as that is the intersection point, but this book (Schaum's Probability Outlines) says that A\capB=[-3,8)...

someome please help me with this problem: "Any real numbers x and y with 0 < x < y, there exist positive integers p and q such that the irrational number s =( p√2)/q is in the interval (x; y)."

Homework Statement Let K be the closed interval [0,1] and consider the function f(x)=x^2. Is f convex? Is f linear? help please :/ i don't even know how to set this up to check, our teacher didn't even get to this in class yet! Homework Equations The Attempt at a Solution

2nd order DE..."largest interval" confusion Homework Statement Determine the largest t-interval on which therem 3.1 guarantees the existence of a unique solution: y'' + 3t^2y' + 2y = sin(t) ...y(1) = 1 ...y'(1) = -1 Homework Equations theroem 3.1 is the one that states if p(t)...

Homework Statement The position of a particle in meters moving along the x-axis is given by: x=21+22t-6t^2 Calculate the average velocity of the object in m/s during the time interval t=1s to t=3s. Homework Equations x=21+22t-6t^2 t=3 ; t=1 v avg. = Xf - Xi/Tf - Ti = Δx/Δt don't...

Homework Statement If R1 and R2 are two uniformly distributed random variables on the interval [0,1]. What is the density function Z=R1*R2? Homework Equations I'm not sure actually The Attempt at a Solution I have tried to manipulate with moment generating function (which i...

A FAQ is why the spacetime interval has a minus sign. A geometrical answer is that the interval is always the shortest path (the straight line) between two points. If we talk about spatial points, that interval is the hypotenuse of a right angle triangle, whose sides are the projections of...

Homework Statement show that the interval (0,1) is uncountable iff \mathbb{R} is uncountable. The Attempt at a Solution Can I take the interval (0,1) and multiply it by a large number and then a large number and eventually extend it to the whole real line. So now (0,1) can be...

Homework Statement State the meaning of {x:-4<x≤10} in words. Express the set {x:-4<x≤10} using interval notation and draw it on a number line. Homework Equations The Attempt at a Solution My attempt. The meaning of {x:-4<x≤10} is that all the numbers of X, are greater than -4...

Homework Statement Fidn the Fourier expansion for f of period 2Pi that corresponds to y=x/3 on the interval [0,2Pi) Im just a little confused about if I am setting up the integration properly. The asymmetric interval is kind of confusing me here. The Attempt at a Solution a0 = 1/Pi ∫ x/3 dx =...

Here is an equation from proof of invariance of interval: This equation is from bernard schutz's first course in GR: I could not understand what M stands for. Can someone help me with this? I don't have advanced knowledge. I am a beginner UG.

∫0->∞ x/(x^3 + 1) dx. Use comparison theorem to determine whether the integral is convergent of divergent. Homework Equations None. The Attempt at a Solution ∫0->∞ x/(x^3 + 1) dx = ∫0->∞ x/(x^3) dx = ∫0->∞ 1/(x^2) dx From my class I learned that ∫1->∞ 1/(x^2) dx , is convergent But...

The interval between two events ds^2 = -(cdt)^2 + x^2 + y^2 + z^2 is invariant in inertial frames. I was wondering, if this same interval still applies and is invariant in non-inertial frames?

If f is differentiable on [a,b] and f'(c)>0 for some a<c<b then does this imply that f is monotonically increasing on some neighborhood of c? My intuition says yes but I just can't figure out a way to prove it. (not homework). Because of the weierstrass function I'm pretty sure...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Hello, I'm doing some nonlinear regression fitting, and I have a set of data with n data points and I am fitting the data to a model which contains 3 parameters. I can get a confidence interval from the program I'm using for each parameter, but how can I calculate the standard deviation for...

Hi people, Time-dependent perturbation theory allows for transitions to excited states, through a sinusoidal perturbation whose frequency is smaller than the energy difference between the states. (That is, P_{a \rightarrow b}=\frac{sin^{2}[(\omega_{0}-\omega)t/2]}{(\omega_{0}-\omega)^2}...

Let f:[a,b]\rightarrowR be continuous on [a,b] and differentiable in (a,b). Show that if lim f'(x)=A as x goes to a then f'(a) exist and equals A. So I was thinking this has to do either with the mean value theorem or Darboux's Theorem. I have that f(b)-f(a)=f'(c)(b-a) by the mean...

I (think I) understand that: 1. With the Schwarzschild metric, the ratio of proper time to coordinate time decreases ("clock runs slower") with decreasing radial distance. (And ratio of proper distance to coordinate distance increases.) 2. The geodesic path followed by a freely falling...

Let I be an open interval and f : I → ℝ is a function. How do you define "f is continuous on I" ? would the following be sufficient? : f is continuous on the open interval I=(a,b) if \stackrel{lim}{x\rightarrow}c \frac{f(x)-f(c)}{x-c} exists \forall c\in (a, b) is this correct? Also, what...

Showing the inequality holds for an interval (?) Homework Statement Hi, my homework question is: Show that the inequality \sqrt{2+x}<2+\frac{x}{4} holds \forallx\in[-2,0] Homework Equations The Attempt at a Solution I tried using IVT or bisection method, but they are just for...

Homework Statement Janet sells cookware at home parties, she wants to estimate the average amount a client spends at each party. A random sample of 35 receipts gave a mean of X bar = $34.70 with standard deviation s = %4.85. a) find a 90% confidence interval for the average amount spent by...

Homework Statement Find the interval of convergence of each of the following Ʃ^{∞}_{n=0} (\frac{3^{n}-2^{2}}{2^{2n}}(x-1)^{n}) Homework Equations Please refer to attachment The Attempt at a Solution Please refer to attachment. All I want to know is that I'm doing this problem...

why arent non continuous functions in an interval a linear space?

Homework Statement Suppose that total population inversion could be achieved in a ruby laser. If half of the electrons in E2 could then drop to E1 in 30 ns, what would be the avg power of the resulting laser pulse over this time interval? Assume that the ruby crystal is a cylinder 5.00cm long...

Homework Statement If a and b are positive numbers, find the maximum value of f(x) = x^a(1 - x)^b on the interval 0 ≤ x ≤ 1.? Homework Equations f'(x) = x^a . -b(1-x)^(b-1) + (1-x)^b . ax^(a-1) The Attempt at a Solution I know to set f'(x) = 0 but I'm not sure how I'm supposed to tidy up...

CALCULUS, EXTREME VALUES of function on interval and where they occur! find the extreme value of function on the interval and where they occur. Please Help, teacher did during class but didnt get explanation. 1. y=cos(x-(pi/4)) , at the interval of [0,7pi/4] My attempt: y'= -sin...

Registered events X in time interval t are distributed linearly n = n0 + bt. Find probability density function, then t = 10, n0 = 5 and b =2. Find average amount of registered events per day and Mean squared error. Find the probability to register an event per 5th and 6th days. What is the...

Apostol in his "Mathematica Analysis" defines something called a "component interval". However, I cannot find it anywhere on google or in other books I have on analysis, and I really would like to see a picture of what he means.. Apostol's definition is that the component interval of an open...

The question is as follows: Prove that if I1, I2 are intervals and J = I1\capI2 then J is an interval. To be honest I don't even know where to start. There's a "hint" that suggests that I first write out the definitions of I1, I2, J as intervals and of the intersection between I1 and I2, but...

Homework Statement i was doing this exercise and came across this example. ∞ Ʃ (x^n)/ln(n+1) n=1 The Attempt at a Solution i know you have to do the ratio test which is lim | a(n+1)/a(n)| n>∞ i got to lim | [x ln(n+1)] /ln(n+2) | n>∞ and have no idea how to continue? is...

Homework Statement I've attached the question Homework Equations The Attempt at a Solution I'm not exactly sure how to do this question. Is it an interval of convergence question where i simply let log(1+2x) < 1 and solve for x??

Homework Statement Let X1, X2,...Xn be a random sample from the distribution with probability density function fX (x;θ) = (θ+1)(1-x)θ, 0<x<1 θ>-1 a) What is the probability distribution of Y= -\sum ln(1-Xi from i=1 -> n b) Suggest a (1-α)100% confidence interval for θ based on Y=...

Homework Statement Show that the function f: J → ℝ is bounded if f is uniformly continuous on the bounded interval J. Homework Equations J is a bounded interval, so say J = (a,b) f is uniformly continuous on J, so \forall \epsilon > 0 there exists a \delta > 0 such that for s,t \in J...

The problem is: lim as x→- ∞ (-5x/x-2)=-5 And I have to find the best interval of solutions for N Relevant equations: if x>N then |(-5x/x-2)-(-5)|<ε My attempt: |(-5x/x-2) - (-5)|<ε |-10/x-2|<ε x-2< 10/ε as x→-∞ we can assume that x-2<0 x-2<10/ε x< (10/ε)+2...

Hi guys! Excuse the spam, but I would like to ask something which I read in Armstrongs Basic Topology which I am just not 100% sure about. He says we wish to define homeomorphism such that a circle cannot be homeomorphic to an interval such as [0,1). A continuous function f : X \mapsto Y is...

Homework Statement Suppose that the function f|(a,b)→ℝ is uniformly continuous. Prove that f|(a,b)→ℝ is bounded. Homework Equations A function f|D→ℝ is uniformly continuous provided that whenever {un} and {vn} are sequences in D such that lim (n→∞) [un-vn] = 0, then lim (n→∞) [f(un) -...

1. The problem statement: In what region can we choose x0 and get convergence to the root x = 0 for f(x) = e-1/x^2 Homework Equations xn+1 = xn - f(xn) / f'(xn) The Attempt at a Solution The only thing I've come across is a formula that says |root - initial point| < 1/M where M =...

Homework Statement Find the power series representation for the function f(x)=x/(x^2-3x+2) and determine the interval of convergence. Homework Equations The Attempt at a Solution First I separate into partial fractions 2/(x-2) - 1/(x-1) 2/(x-2) = sum n=0 to infinity (x/2)^n...

2 travelining in a straight line initial velocity is 14m/s, at a constant acceleration of 2.0m/s^2 to a velocity of 24 m/s a) how much time to reach velocity of 24m/s t= v-v0/a or 24-14/2= 5 seconds b) distance covered by car in this process? d=v0(t) + 1/2(at^2) or...

Using Mathematica, I need to define a discrete probability distribution of N equally spaced angles on the interval [0, 2Pi], which isn't exactly uniform. More precisely, I need the distribution to feature a "Poisson-like" behavior : the angles should be randomly selected by random "packs"...

Homework Statement Let E be the set of points in [0,1) whose decimal expansion contains somewhere the block 55555. Find the measure of E. Homework Equations The Attempt at a Solution I have a feeling that in order to find the measure of E, I should find the measure of the...

Hey everyone, This is a review of some stuff I learned in high school, but I haven't actually done anything calculus related in about 2 years, and to be honest it looks foreign to me, if someone could help jog the old noodle it would help tremendously. The first question is as follows...

Is this a good-enough proof? I could have used neighborhoods to show this, but it seems like this way is a bit easier. http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110911_113143.jpg

All the events that are connected with a particular "Event 1" by spacelike intervals lie outside the past and future light cones of Event 1. But in some other frame of reference these events which are connected to Event 1 by spacelike intervals can appear to occur simultaneously with Event 1...

Homework Statement What will be the values of 'm' so that the range of the equation y= \frac{mx^2+3x-4}{-4x^2+3x+m} will be all real values i.e. y\epsilon (-\infty,\infty)given:x can take all real values. any help or hint will be appreciated. Homework Equations The Attempt at a Solution i...